Because language really, really matters. It is fundamental to how we construct and convey meaning. And when that meaning is: "I am expressing paternalistic concern at your inability [as a woman] to rein in your emotion" then yes, that is sexist and yes, it is a big deal. To undermine her anger as hysteria, to reference her femaleness, is a particularly male way of putting a woman down.Going on to link Cameron's comment to the Sky Sports sexism furore a couple of months ago, Brooks makes the point that sexist banter exists in a world where these notions aren't challenged and how we shouldn't let people (usually) men get away with this dismissive and demeaning language.
A wider point here is that taken out of context, the word dear probably isn't that bad - it's certainly not on the same level as many of the frequent, offensive terms used daily - bitch, cow, slag and the like - but it's the context that imbues it with its offence. It's the way its use represents a stance on the part of the speaker ("I am in a superior position to you and can address you in whatever way I choose") and ties in to a broader picture of social inequality - Cameron and his chums are largely the product of single-sex boarding schools, who treat gender equality as a hilarious wheeze, rather than an issue to be taken seriously - that make it such an inflammatory language act.
Edited to add comma in title - apologies for punctuation fail